Two-stage sampling in surveys to substantiate freedom from disease

Area of Science:

• Veterinary epidemiology
• Statistical modeling
• Livestock health surveillance

Background:

• Livestock diseases often exhibit herd-level clustering.
• Traditional simple random sampling is inadequate for large, clustered populations.
• Two-stage sampling is commonly used but complicates sample size calculations.

Purpose of the Study:

• To develop a probability formula for sample-size calculation in two-stage livestock surveys.
• To optimize survey costs by determining the most economical combination of first-stage (herd) and second-stage (animal) sample sizes.
• To account for imperfect diagnostic tests and finite population sizes in sample-size determination.

Main Methods:

• Development of a probability formula for two-stage sampling, initially assuming perfect test accuracy.
• Simulation studies to validate the initial formula.
• Application of an exact-probability formula incorporating imperfect tests and finite populations.
• Utilizing the FreeCalc computer program for practical implementation.

Main Results:

• The developed formula allows for the calculation of least-cost survey designs by adjusting first- and second-stage sample sizes.
• Simulation validated the formula's accuracy in determining optimal sample size combinations.
• The exact-probability formula provides a more realistic approach by considering test imperfections and population size.

Conclusions:

• The new probability formula effectively addresses sample-size calculation challenges in two-stage livestock surveys.
• Implementing the formula with tools like FreeCalc enables cost-effective survey design for disease surveillance.
• This approach enhances the efficiency and accuracy of livestock disease monitoring.